Problem 0 - Introduction

Index

Your first assignment is to read pp 1-11 from Chapter 1 of Dorwat's The Geometry of Incidence. Please be sure you understand the important terms listed below. In addition, try to answer the following questions.

Important Terms and concepts:

• Incidence
• Topology
• Geometry
• Point
• Line
• Parallel
• Non-Euclidean Geometry
• Klein's Erlangen Program
• Invariant
• Transformation
• Congruent

Please Answer the Following Questions:

1. Why is it helpful to use the concept of incidence when describing geometric figures?
2. Why do geometers often disregard the concept of parallel lines when evaluating incidences in geometric figures?
3. What is geometry? How are the parts of the subject characterized?
4. Are all geometries either Euclidean or non-Euclidean?
5. What is Euclidean geometry?
6. Explain Klein's principle of geometry.
7. Explain the "pulling and stretching without breaking or tearing" approach to topology. What are the invariants? In topology, are all triangles congruent?